Consider the pseudo-octahedral complex ion of \(\mathrm{Cr}^{3+}\) , where A and \(\mathrm{B}\) represent ligands. Ligand A produces a stronger crystal field than ligand B. Draw an appropriate crystal field diagram for this complex ion (assume the A ligands are on the \(z\) -axis).

Pseudo-octahedral means the arrangement of six ligands around a central metal ion resembles the octahedral shape with some distortions. In this case, four ligands are found in the plane, and two other ligands are located above and below the central metal ion (on the z-axis).

In an octahedral complex, the d-orbitals (\(d_{xy}\), \(d_{xz}\), \(d_{yz}\), \(d_{x^2-y^2}\), and \(d_{z^2}\)) are split into two groups: \(t_{2g}\) and \(e_g\). The \(t_{2g}\) group includes \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\) orbitals, whereas the \(e_g\) group includes \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals.

Since A ligands produce a stronger crystal field than B ligands, and A ligands are on the z-axis, the corresponding crystal field diagram should have a larger splitting energy (\(\Delta\)) between \(t_{2g}\) and \(e_g\) orbitals. Place three B ligands in the xy plane and the two A ligands on the z-axis.

To draw the crystal field diagram: 1. Plot the energy levels for the \(t_{2g}\) and \(e_g\) orbitals. 2. Indicate the larger splitting energy for the A ligands on the z-axis (i.e., the \(\Delta\) between \(t_{2g}\) and \(e_g\) is larger for A ligands). 3. Label the orbitals that belong to the \(t_{2g}\) and \(e_g\) groups. 4. Place the B ligands in the plane and A ligands above and below the central metal ion. 5. Draw arrows to show the field splitting by the A and B ligands (considering the larger splitting produced by the A ligands). The crystal field diagram will show two A ligands on the z-axis (higher repulsion with \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals) and three B ligands in the xy plane. This causes a larger splitting between \(t_{2g}\) and \(e_g\) orbitals due to the stronger crystal field of the A ligands.